Novel interval theory‐based parameter identification method for engineering heat transfer systems with epistemic uncertainty

Abstract

Summary The parameter identification problem with epistemic uncertainty, where only a small amount of experimental information is available, is a challenging issue in engineering. To overcome the drawback of traditional probabilistic methods in dealing with limited data, this paper proposes a novel interval theory‐based inverse analysis method. First, the interval variables are introduced to represent the input uncertainties, whose lower and upper bounds are to be identified. Subsequently, an unbiased estimation method is presented to quantify the experimental response interval from limited measurements. Meanwhile, a quantitative metric is defined to characterize the relative errors between computational and experimental response intervals by which the interval parameter identification can be constructed as a nested‐loop optimization procedure. To improve the computational efficiency of response prediction with respect to various interval variables, a universal surrogate model is established in the support box via Legendre polynomial chaos expansion, where the expansion coefficients can be evaluated by a collocation method under Clenshaw‐Curtis points and Smolyak algorithm. Eventually, a heat conduction example is provided to verify the feasibility of proposed method, especially in the case with noise‐contaminated temperature measurements.

Novel solution framework for inverse problem considering interval uncertainty

“…Based on the interval model, a kind of uncertain inverse method called the interval inverse method has been proposed 15,16 . The interval inverse method is widely used in parameter identification, model updating, damage detection and dynamic load identification fields, and they are mainly linear structural or system problems 17–19 . In the process of solving the linear problem, the response intervals can be obtained through interval arithmetic.…”

Reliability assessment for failure‐dependent and uncertain systems: A Bayesian network based on copula method and probability‐box

“…Conversely, epistemic uncertainty is subjective uncertainty, which arises from lack of information. Some methods have been employed to address epistemic uncertainty, for example, interval probability, 11,12 probability‐box (p‐box), 13–15 evidence theory, 16–18 fuzzy set, 19 BN inference, 20 etc. Based on those epistemic uncertainty quantification methods, some comprehensive works have been performed by Mi et al, 21 those works have integrated epistemic uncertainty and dependent failures especially common cause failures into system reliability model based on universal generation function, 21 BN, 22,23 and evidential network 2,24 …”

Load Identification Method Based on Interval Analysis and Tikhonov Regularization and Its Application

“…Domestic and foreign scholars have made some achievements in the research of load identification based on the interval analysis method. Wang and Matthies [9] proposed a novel model calibration method that combines nonprobabilistic interval technology with Bayesian analysis theory, and the feasibility of the proposed method is demonstrated using the renowned Sandia thermal challenge problem. Wang and Matthies and Wang et al [10,11] proposed a novel model validation approach by using evidence theory.…”